Figure 1: (Top) The red curve is a sawtooth ``wave'' encountered in electronics. The black curve is the sum of the first six terms of the Fourier series and can be seen to approximate the sawtooth quite closely, except for overshooting near the discontinuities. As more terms are included, the approximation becomes better and better. (Bottom) Here are shown the first six terms of the Fourier series which, when added together, yield the black curve shown at the top.